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<meta name="description" content="MATLAB代码清风课代码12345678910111213141516171819function [W] = Entropy_Method(Z)% 计算有n个样本，m个指标的样本所对应的的熵权% 输入% Z ： n*m的矩阵（要经过正向化和标准化处理，且元素中不存在负数）% 输出% W：熵权，m*1的行向量%% 计算熵权    [n,m] = size(Z);    D = zeros(1,m">
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<meta property="og:description" content="MATLAB代码清风课代码12345678910111213141516171819function [W] = Entropy_Method(Z)% 计算有n个样本，m个指标的样本所对应的的熵权% 输入% Z ： n*m的矩阵（要经过正向化和标准化处理，且元素中不存在负数）% 输出% W：熵权，m*1的行向量%% 计算熵权    [n,m] = size(Z);    D = zeros(1,m">
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<meta name="twitter:description" content="MATLAB代码清风课代码12345678910111213141516171819function [W] = Entropy_Method(Z)% 计算有n个样本，m个指标的样本所对应的的熵权% 输入% Z ： n*m的矩阵（要经过正向化和标准化处理，且元素中不存在负数）% 输出% W：熵权，m*1的行向量%% 计算熵权    [n,m] = size(Z);    D = zeros(1,m">



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        <h2 id="MATLAB代码"><a href="#MATLAB代码" class="headerlink" title="MATLAB代码"></a>MATLAB代码</h2><h3 id="清风课代码"><a href="#清风课代码" class="headerlink" title="清风课代码"></a>清风课代码</h3><figure class="highlight matlab"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">function</span> <span class="params">[W]</span> = <span class="title">Entropy_Method</span><span class="params">(Z)</span></span></span><br><span class="line"><span class="comment">% 计算有n个样本，m个指标的样本所对应的的熵权</span></span><br><span class="line"><span class="comment">% 输入</span></span><br><span class="line"><span class="comment">% Z ： n*m的矩阵（要经过正向化和标准化处理，且元素中不存在负数）</span></span><br><span class="line"><span class="comment">% 输出</span></span><br><span class="line"><span class="comment">% W：熵权，m*1的行向量</span></span><br><span class="line"></span><br><span class="line"><span class="comment">%% 计算熵权</span></span><br><span class="line">    [n,m] = <span class="built_in">size</span>(Z);</span><br><span class="line">    D = <span class="built_in">zeros</span>(<span class="number">1</span>,m);  <span class="comment">% 初始化保存信息效用值的行向量</span></span><br><span class="line">    <span class="keyword">for</span> <span class="built_in">i</span> = <span class="number">1</span>:m</span><br><span class="line">        x = Z(:,<span class="built_in">i</span>);  <span class="comment">% 取出第i列的指标</span></span><br><span class="line">        p = x / sum(x);</span><br><span class="line">        <span class="comment">% 注意，p有可能为0，此时计算ln(p)*p时，Matlab会返回NaN，所以这里我们自己定义一个函数</span></span><br><span class="line">        e = -sum(p .* mylog(p)) / <span class="built_in">log</span>(n); <span class="comment">% 计算信息熵</span></span><br><span class="line">        D(<span class="built_in">i</span>) = <span class="number">1</span>- e; <span class="comment">% 计算信息效用值</span></span><br><span class="line">    <span class="keyword">end</span></span><br><span class="line">    W = D ./ sum(D);  <span class="comment">% 将信息效用值归一化，得到权重    </span></span><br><span class="line"><span class="keyword">end</span></span><br></pre></td></tr></table></figure>
<h2 id="python代码"><a href="#python代码" class="headerlink" title="python代码"></a>python代码</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br></pre></td><td class="code"><pre><span class="line"></span><br><span class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</span><br><span class="line"></span><br><span class="line"><span class="keyword">import</span> pandas <span class="keyword">as</span> pd</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">PositiveMinToMax</span><span class="params">(datas)</span>:</span></span><br><span class="line">    <span class="keyword">return</span> np.max(datas) - datas  <span class="comment"># 套公式</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="comment"># 中间型指标 -&gt; 极大型指标</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">PositiveMidToMax</span><span class="params">(datas, x_best)</span>:</span></span><br><span class="line">    temp_datas = datas - x_best</span><br><span class="line">    M = np.max(abs(temp_datas))</span><br><span class="line">    answer_datas = <span class="number">1</span> - abs(datas - x_best) / M  <span class="comment"># 套公式</span></span><br><span class="line">    <span class="keyword">return</span> answer_datas</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="comment"># 区间型指标 -&gt; 极大型指标</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">PositiveIntToMax</span><span class="params">(datas, x_min, x_max)</span>:</span></span><br><span class="line">    M = max(x_min - np.min(datas), np.max(datas) - x_max)</span><br><span class="line">    answer_list = []</span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> datas:</span><br><span class="line">        <span class="keyword">if</span> i &lt; x_min:</span><br><span class="line">            answer_list.append(<span class="number">1</span> - (x_min - i) / M)  <span class="comment"># 套公式</span></span><br><span class="line">        <span class="keyword">elif</span> x_min &lt;= i &lt;= x_max:</span><br><span class="line">            answer_list.append(<span class="number">1</span>)</span><br><span class="line">        <span class="keyword">else</span>:</span><br><span class="line">            answer_list.append(<span class="number">1</span> - (i - x_max) / M)</span><br><span class="line">    <span class="keyword">return</span> np.array(answer_list)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">Standardize</span><span class="params">(datas, rownum)</span>:</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">0</span>, rownum):</span><br><span class="line">        tmpar = datas[:, i]</span><br><span class="line">        datas[:, i] = tmpar / np.sqrt(sum(tmpar ** <span class="number">2</span>))</span><br><span class="line">    <span class="keyword">return</span> datas</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">entropy_method</span><span class="params">(data)</span>:</span></span><br><span class="line"></span><br><span class="line">    P = data / data.sum(axis=<span class="number">0</span>)</span><br><span class="line"></span><br><span class="line">    <span class="comment"># 计算熵值</span></span><br><span class="line">    E = np.nansum(-P * np.log(P) / np.log(len(data)), axis=<span class="number">0</span>)</span><br><span class="line"></span><br><span class="line">    <span class="comment"># 计算权系数</span></span><br><span class="line">    <span class="keyword">return</span> (<span class="number">1</span> - E) / (<span class="number">1</span> - E).sum()</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">main</span><span class="params">()</span>:</span></span><br><span class="line">    df = pd.read_csv(<span class="string">"20条河流的水质情况数据.csv"</span>)</span><br><span class="line"></span><br><span class="line">    ans1 = df.values</span><br><span class="line"></span><br><span class="line">    m, n = ans1.shape</span><br><span class="line"></span><br><span class="line">    ans2 = np.array([ans1[:, <span class="number">0</span>], PositiveMidToMax(ans1[:, <span class="number">1</span>], <span class="number">7</span>),PositiveMinToMax(ans1[:, <span class="number">2</span>]),</span><br><span class="line">                     PositiveIntToMax(ans1[:, <span class="number">3</span>], <span class="number">10</span>, <span class="number">20</span>)])</span><br><span class="line"></span><br><span class="line">    ans3 = np.array(ans2).T</span><br><span class="line"></span><br><span class="line">    ans4 = Standardize(ans3, n)</span><br><span class="line"></span><br><span class="line">    ans7 = entropy_method(ans4)</span><br><span class="line"></span><br><span class="line">    print(ans7)</span><br><span class="line"></span><br><span class="line">    D_P = np.sqrt((np.power(ans4 - np.tile(ans4.max(axis=<span class="number">0</span>), (m, <span class="number">1</span>)), <span class="number">2</span>) * ans7).sum(axis=<span class="number">1</span>))</span><br><span class="line">    D_N = np.sqrt((np.power(ans4 - np.tile(ans4.min(axis=<span class="number">0</span>), (m, <span class="number">1</span>)), <span class="number">2</span>) * ans7).sum(axis=<span class="number">1</span>))</span><br><span class="line"></span><br><span class="line">    S = D_N / (D_P + D_N)</span><br><span class="line"></span><br><span class="line">    S_std = S / sum(S)</span><br><span class="line"></span><br><span class="line">    print(S_std)</span><br><span class="line"></span><br><span class="line">    sorted_S = np.sort(S_std)[::<span class="number">-1</span>]</span><br><span class="line"></span><br><span class="line">    S_std = np.expand_dims(S_std,axis=<span class="number">1</span>)</span><br><span class="line"></span><br><span class="line">    sorted_S = np.expand_dims(sorted_S, axis=<span class="number">1</span>)</span><br><span class="line"></span><br><span class="line">    out_S = np.hstack((ans4, S_std))</span><br><span class="line"></span><br><span class="line">    out_S = np.hstack((out_S,sorted_S))</span><br><span class="line"></span><br><span class="line">    print(out_S)</span><br><span class="line"></span><br><span class="line">    np.savetxt(<span class="string">"a.csv"</span>,out_S,delimiter=<span class="string">','</span>)</span><br><span class="line"></span><br><span class="line">    column = [<span class="string">'含氧量（ppm)'</span>,<span class="string">'PH值'</span>,<span class="string">'细菌总数(个 / mL)'</span>,<span class="string">'植物性营养物量（ppm)'</span>,<span class="string">'得分'</span>]</span><br><span class="line"></span><br><span class="line">    pd_data = pd.DataFrame(out_S,columns=column)</span><br><span class="line"></span><br><span class="line">    pd_data.to_csv(<span class="string">'b.csv'</span>)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">main()</span><br></pre></td></tr></table></figure>
      
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